Thanks so much PropellerHead - I was trying to describe the one-off hard shift into second (only on cold starting) firstly to my regular shop guys, and also on this board once; sounds like I had the same issue with my '06 4.8iS, however now there is a shudder between 3-4 at > 3,000 rpm, without such a hard lurch into 2nd, but this could be a separate issue!
Another E53 owner with a daughter at my kids school tipped me off about a local guy called 'Mike the Mechanic' here in Abu Dhabi who is an X5 owner, as you say - I talked to him today and he said the same about diagnosing problems with engine management and sensors before offering to strip and rebuild the Tranny. I'm also thinking hard about the possible financial consequences (the wife is 60% made up to make me get a Tahoe, I'm sure) but he seems a straight-up guy, so will go for it in the coming week - after pay-day, of course